They therefore distinguished between them by saying that an essential attribute is conceived before the essence is conceived, so that the thing itself cannot be understood without it, unlike an attribute inseparable from the essence.

Both essential and accidental attributes may be shared throughout a genus, yielding the general genus and the common accident; or exclusive to a species, yielding the differentia and the distinctive property; or combine what is shared with what distinguishes, yielding the species. These, then, are the “five universals”: genus, differentia, species, distinctive property, and common accident. Discussing these attributes and their divisions is chiefly useful for definitions and the essential realities of things.

As for the syllogism, it is a statement composed of statements which, if conceded, necessarily entail another statement by virtue of themselves. It must contain two premises. A “premise” is a proposition—that is, a declarative sentence—and must contain two simple terms. The discussion thus proceeds on three levels:

(First) The discussion of simple terms, their expressions and meanings: signification by correspondence, inclusion, and necessary implication; synonymous, distinct, equivocal, and univocal names; simple and compound expressions; and the universal and the particular.

The “second level” concerns propositions and their divisions: particular, universal, and unqualified propositions; affirmation and negation; and the modalities of propositions. It also concerns the rules governing propositions, such as the falsity of the contradictory and the truth of the converse and the contrapositive.